Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 3 Sayı: 1, 8 - 16, 10.06.2020
https://doi.org/10.33401/fujma.708816

Öz

Kaynakça

  • [1] A. Pressley, Elementary Differential Geometry, 2nd ed., Springer, 2010.
  • [2] M. P. do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Courier Dover Publications, 2016.
  • [3] M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd ed., Publish or Perish, Houston, Texas, 1999.
  • [4] R. S. Millman, G. D. Parker, Elements of Differential Geometry, Prentice-Hall, Inc., New Jersey, 1977.
  • [5] B. Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly, 110 (2003), 147–152.
  • [6] B. Y. Chen, Rectifying curves and geodesics on a cone in the Euclidean 3-space, Tamkang J. Math., 48 (2017), 209-214.
  • [7] B. Y. Chen, F. Dillen, Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Acad. Sinica, 33 (2005), 77-90.
  • [8] S. Deshmukh, B. Y. Chen, S. Alshamari, On rectifying curves in Euclidean 3-space, Turk. J. Math., 42 (2018), 609-620.
  • [9] K. Ilarslan, E. Nésovic, Timelike and null normal curves in Minkowski space E31, Indian J. Pure Appl. Math., 35(7) (2004), 881-888.
  • [10] K. Ilarslan, E. Nésovic, On rectifying curves as centrodes and extremal curves in the Minkowski 3-Space, Novi Sad J. Math., 37 (2007), 53-64.
  • [11] K. Ilarslan, E. Nésovic, T. M. Petrovic, Some characterization of rectifying curves in the Minkowski 3-Space, Novi Sad J. Math., 33 (2003), 23-32.
  • [12] R. Lopez, Differential Geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 7(1) (2014), 44–107.
  • [13] B. O’Neill, Semi–Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.

Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$

Yıl 2020, Cilt: 3 Sayı: 1, 8 - 16, 10.06.2020
https://doi.org/10.33401/fujma.708816

Öz

A rectifying curve $\gamma$ in the Euclidean $3$-space $\mathbb{E}^3$ is defined as a space curve whose position vector always lies in its rectifying plane (i.e., the plane spanned by the unit tangent vector field $T_\gamma$ and the unit binormal vector field $B_\gamma$ of the curve $\gamma$), and an $f$-rectifying curve $\gamma$ in the Euclidean $3$-space $\mathbb{E}^3$ is defined as a space curve whose $f$-position vector $\gamma_f$, defined by $\gamma_f(s) = \int f(s) d\gamma$, always lies in its rectifying plane, where $f$ is a nowhere vanishing real-valued integrable function in arc-length parameter $s$ of the curve $\gamma$. In this paper, we introduce the notion of $f$-rectifying curves which are null (lightlike) in the Minkowski $3$-space $\mathbb{E}^3_1$. Our main aim is to characterize and classify such null (lightlike) $f$-rectifying curves having spacelike or timelike rectifying plane in the Minkowski $3$-Space $\mathbb{E}^3_1$.

Kaynakça

  • [1] A. Pressley, Elementary Differential Geometry, 2nd ed., Springer, 2010.
  • [2] M. P. do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Courier Dover Publications, 2016.
  • [3] M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd ed., Publish or Perish, Houston, Texas, 1999.
  • [4] R. S. Millman, G. D. Parker, Elements of Differential Geometry, Prentice-Hall, Inc., New Jersey, 1977.
  • [5] B. Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly, 110 (2003), 147–152.
  • [6] B. Y. Chen, Rectifying curves and geodesics on a cone in the Euclidean 3-space, Tamkang J. Math., 48 (2017), 209-214.
  • [7] B. Y. Chen, F. Dillen, Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Acad. Sinica, 33 (2005), 77-90.
  • [8] S. Deshmukh, B. Y. Chen, S. Alshamari, On rectifying curves in Euclidean 3-space, Turk. J. Math., 42 (2018), 609-620.
  • [9] K. Ilarslan, E. Nésovic, Timelike and null normal curves in Minkowski space E31, Indian J. Pure Appl. Math., 35(7) (2004), 881-888.
  • [10] K. Ilarslan, E. Nésovic, On rectifying curves as centrodes and extremal curves in the Minkowski 3-Space, Novi Sad J. Math., 37 (2007), 53-64.
  • [11] K. Ilarslan, E. Nésovic, T. M. Petrovic, Some characterization of rectifying curves in the Minkowski 3-Space, Novi Sad J. Math., 33 (2003), 23-32.
  • [12] R. Lopez, Differential Geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 7(1) (2014), 44–107.
  • [13] B. O’Neill, Semi–Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Zafar Iqbal 0000-0003-4405-1160

Joydeep Sengupta Bu kişi benim 0000-0002-1609-0798

Yayımlanma Tarihi 10 Haziran 2020
Gönderilme Tarihi 24 Ocak 2020
Kabul Tarihi 15 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

APA Iqbal, Z., & Sengupta, J. (2020). Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$. Fundamental Journal of Mathematics and Applications, 3(1), 8-16. https://doi.org/10.33401/fujma.708816
AMA Iqbal Z, Sengupta J. Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$. FUJMA. Haziran 2020;3(1):8-16. doi:10.33401/fujma.708816
Chicago Iqbal, Zafar, ve Joydeep Sengupta. “Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$”. Fundamental Journal of Mathematics and Applications 3, sy. 1 (Haziran 2020): 8-16. https://doi.org/10.33401/fujma.708816.
EndNote Iqbal Z, Sengupta J (01 Haziran 2020) Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$. Fundamental Journal of Mathematics and Applications 3 1 8–16.
IEEE Z. Iqbal ve J. Sengupta, “Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$”, FUJMA, c. 3, sy. 1, ss. 8–16, 2020, doi: 10.33401/fujma.708816.
ISNAD Iqbal, Zafar - Sengupta, Joydeep. “Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$”. Fundamental Journal of Mathematics and Applications 3/1 (Haziran 2020), 8-16. https://doi.org/10.33401/fujma.708816.
JAMA Iqbal Z, Sengupta J. Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$. FUJMA. 2020;3:8–16.
MLA Iqbal, Zafar ve Joydeep Sengupta. “Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$”. Fundamental Journal of Mathematics and Applications, c. 3, sy. 1, 2020, ss. 8-16, doi:10.33401/fujma.708816.
Vancouver Iqbal Z, Sengupta J. Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$. FUJMA. 2020;3(1):8-16.

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